Let G be a real semisimple Lie group and X be the complete (complex) flag variety. I will show how to study the orbits of G-action on X using Morse theory. This method is proposed by Mirković, Uzawa and Vilonen. Based on the G-orbit-decomposition, I will prove that the equivariant K-theory K^G(X) is isomorphic to K^U(X), after a shift of dimension, where U is the maximal compact subgroup of G. This gives a proof of the Connes-Kasparov conjecture "on flag variety". If time allows I will also talk about the relation between G-orbits on flag variety and representation theory.